The camp is home to 500,000 refugees - the equivalent of the population of Leicester.
The country's de facto leader, Nobel peace laureate Aung San Suu Kyi, has faced worldwide condemnation for her apparent inaction in the face of the widely alleged reports of atrocities committed against the Rohingya, which the United Nations says might amount to genocide.
Almost 700,000 people have left since the action began last August.
On Sunday Johnson and Suu Kyi "discussed in an open and friendly manner the latest developments in Rakhine State, including planning for the reception of returnees who fled", Myanmar's foreign ministry said in a Facebook post alongside photos of the pair meeting.
Visiting a border refugee camp, the Foreign Secretary said such a return would only be possible if a "political solution" could be found to remove the great danger from going back.
He said: "It is vital that the Rohingya refugees must be allowed to their homes in Rakhine voluntarily, in safety and with dignity, under global oversight, and when the conditions. are right".
Speaking on Saturday after a visit to Cox's Bazar in Bangladesh, where over a million Rohingya Muslim refugees are cramped into crowded and unsafe camps, Boris Johnson expressed his horror at the conditions in which they are living. "We need to make those points together to the government in Nay Pyi Daw".
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Almost 690,000 Rohingya have fled Rakhine and crossed into southern Bangladesh since August, when attacks on security posts by rebels triggered a military crackdown that the United Nations has said may amount to genocide.
Almost 690,000 Rohingya have fled their villages and crossed the border of western Myanmar into Bangladesh since August.
He said: "I spoke to her about my own experience witnessing the awful conditions of the Rohingya refugees in Bangladesh, and my deep concern about their future".
Britain is one of the biggest direct donors of aid for the humanitarian effort to help the refugees.
The Foreign Secretary's trip to Bangladesh - the first such official visit in a decade - comes after almost 700,000 Rohingya Muslims fled a military crackdown, which began last August.
He will go on to Bangkok, Thailand, for talks with Thai Prime Minister Prayut Chan-o-cha.